Summary: Affine Lattice Models 1
Claudio Albanese
Department of Mathematics, Imperial College of Science and Technology, University of London, SW7 2AZ,
London, United Kingdom. mailto:claudio.albanese@imperial.ac.uk
Alexey Kuznetsov
Department of Mathematics, 100 St. George Street, University of Toronto, M5S 3G3, Toronto, Canada.
mailto:kuznecov@math.toronto.edu
Abstract. We introduce a new class of lattice models based on a continuous time Markov chain
approximation scheme for affine processes, whereby the approximating process itself is affine. A
key property of this class of lattice models is that the location of the time nodes can be chosen in
a payoff dependent way and one has the flexibility of setting them only at the relevant dates. Time
stepping invariance relies on the ability of computing node-to-node discounted transition probabilities
in analytically closed form. The method is quite general and far reaching and it is introduced in this
article in the framework of the broadly used single-factor, affine short rate models such as the Vasicek
and CIR models. To illustrate the use of affine lattice models in these cases, we analyze in detail the
example of Bermuda swaptions.
Key words: Interest Rate Models, Affine Models, Birth and Death Processes, Discretization Scheme
JEL Classification: G13
Mathematics Subject Classification (2000): 35Q58, 39A12, 60H30
1 Introduction